Solving 20 Erdős Problems with 20 Codex Accounts Running in Parallel(starfleetmath.com)
starfleetmath.com
Solving 20 Erdős Problems with 20 Codex Accounts Running in Parallel
https://www.starfleetmath.com/
23 comments
This is great feedback (thank you for taking the time), & you especially bring up a fair point on the writeups needing to be more human readable. I'll work on that
what was the leaked proof?
My mouth is agape at the fact that this project
is basically what I have been working on non-stop
for the last three weeks and just yesterday gotten
to the point of evaluating; hats off... I only have
one novel proof (non-Erdos) and 13 first-time
formalizations thus far.
I still like doing maths by pen and paper, but this is fun too.
I still like doing maths by pen and paper, but this is fun too.
Thank you for the kind words! I agree, it's exciting that we can now build advanced AI systems for solving novel math (but i still love pen & paper too)
I was studying Erdos problems by only taking ChatGPT 5.5 outputs and just asking it to keep on attempting to solve it by asking it to go further. I haven't started doing this with chatgpt 5.6 I have some partial results here https://chatgpt.com/g/g-p-69f03400f420819192418b18ca90ffee-d...
What was really interesting is that during the process it was able to find lemmas or theorems that might be related or relevant to be published.
While I was doing that I was also trying to use Aristotle to do the Lean formalization and I have a WIP system to do that at https://github.com/aconsapart/thesisus/
What was really interesting is that during the process it was able to find lemmas or theorems that might be related or relevant to be published.
While I was doing that I was also trying to use Aristotle to do the Lean formalization and I have a WIP system to do that at https://github.com/aconsapart/thesisus/
Who is funding this? Sounds like a fun experiment but that’s a huge amount of compute if I understand correctly.
According to a quick google search:
"He is currently CTO at Xinobi AI, a Japan-based startup developing personal AI agents."
"He is currently CTO at Xinobi AI, a Japan-based startup developing personal AI agents."
This is a self funded weekend project for me. It's not associated with any employer (:
> dedicated 60-vCPU server
How many of these are you paying for out of pocket??
How many of these are you paying for out of pocket??
What kind of harness does the exploration? Where did the corpus of Lean proofs come from? Is the code backing Ton 618 open source?
I've been wanting to experiment with using AI to prove math theorems, but compute is obviously a massive limiting factor here. Are there any plans to open source this?
Isn't this sucking the fun out of math? It's not like we're going to get any tangible benefit out of them, so why not let mathematicians keep their jobs?
The thing about math is we don't usually know what is pure fancy and what is civilization altering until far after the discovery. Once in a while it's a real targeted crack at something practical but most often it's collecting things which seem trial until you use them together and suddenly you have computers running LLMs.
If it were really just about funding people who like math to have fun then it's easy to do forever: just don't have them look at the results and keep paying.
If it were really just about funding people who like math to have fun then it's easy to do forever: just don't have them look at the results and keep paying.
Isn't the pursuit of knowledge alone good enough?
The job of a mathematician is to study mathematics, not to create proofs.
An automatic proof solver doesn't make mathematicians obsolete any more than the excel sheet made accountants obsolete.
An automatic proof solver doesn't make mathematicians obsolete any more than the excel sheet made accountants obsolete.
This project, and similar “brute force the knowledge graph” efforts gives “The Nine Billion Names of God” vibes.
https://en.wikipedia.org/wiki/The_Nine_Billion_Names_of_God
https://en.wikipedia.org/wiki/The_Nine_Billion_Names_of_God
or get those bright minds out of academia daycare and back to more actionable needs such as steering agents
This will keep happening until we stop people from doing it.
Get the looms while you're at it
Second, the proofs -- I understand the Lean 4 proofs to be refereed by Fable, and generated by Chat 5.6 Sol. Unlike the leaked proof of the Cycle Double Cover Conjecture last week which had a very nicely readable nearly humanlike writeup, the proof summaries (from Fable) read like Claude tends to read to me these days - real difficulty with the theory of mind of the reader, they are filled with technical phrases, acknowledgment of hard bits and oblique reference to solutions. In short, they suck. I didn't see the word load-bearing, but I bet it's there.
That said, a Lean 4 proof is a pretty compelling output artifact. I find it interesting that it's an additional type of effort to turn these into human readable / appreciable / beautiful / non-shitty proofs.
To those who say who cares -- indeed. But. One of the major reasons things like the Erdos problems are valuable is that they can at times spur new techniques and concepts. The best of these concepts are applied elsewhere, advancing the frontier. While we gain a lot from solving these problems, we'll gain even more from that next step of distillation / explanation into something humans and computers can grok together. I'd hope that with so many tentatively marked 'solved' we will see some new techniques / ontology / concepts. If not, still pretty amazing.